Discussion of paper by Ming Xu, Tao Chen and Xianhui Yang “The effect of parameter uncertainty on achieved safety integrity of safety system”, Reliab. Eng. Syst. Saf., 99 (2012) 15–23

Consider a system consisting of n components each with its own positive integer-valued random weight (capacity). The system is assumed to have a performance level above c if there are at least k working components, and the total weight of all working components is above c. We study the reliability properties of such a system. A recursive formula is obtained for computing the system state probabilities. We present a Monte-Carlo simulation algorithm to observe the time spent by the system in state c or above. The algorithm is based on the use of ordered lifetimes of components. We illustrate the results with numerical computations.